Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.4 - Linear Functions and Slope - Exercise Set - Page 213: 84

Answer

The $y$ intercept of the line is $-3$.

Work Step by Step

Consider a line that passes through the point $\left( 2,-6 \right)$ and has a slope of $-\frac{3}{2}$. Substitute $\left( {{x}_{1}},{{y}_{1}} \right)=\left( 2,-6 \right)$ and $m=-\frac{3}{2}$ (the slope of the given line) in the equation: $\begin{align} & y-\left( -6 \right)=-\frac{3}{2}\left( x-2 \right) \\ & y+6=-\frac{3}{2}x+3 \end{align}$ Solve the above equation for $y$: $\begin{align} & y+6=-\frac{3}{2}x+3 \\ & y=-\frac{3}{2}x+3-6 \\ & y=-\frac{3}{2}x-3 \end{align}$ Compare the last equation with the slope–intercept form $y=mx+b$ of the equation of a line in slope intercept form $b=-3$ Thus, the $y$ intercept of the given line is $b=-3$.
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